Christine Armario listed several of these Frustables (i.e., frustrating Imponderables), but none generated as much email as this one. I thought I'd share some of the correspondence because it shows some of the pitfalls of this kind of research.

Most of the research I've conducted on this subject leads to the conclusion offered by reader Marolyn Woodall:

When a tiny baby becomes hungry, it searches for milk in a nodding motion. If, when it is satisfied, more milk is offered. It learns to refuse by turning from the nipple in a shaking motion.

Sean Hodges offers a variant, which I've also heard before many times:

When babies want to refuse food during spoon feeding, they turn their heads to one side and then the other, as the parent chases their mouths with the spoon. That gives the shake=no.
When babies want something they use buttock-clenches to bounce up and down in their seat, with a compensating nod of the head to keep their balance. That could account for the nod=yes.

We heard from Israeli Yonatan Silver, who offered a theory we had never encountered before, despite the first sentence of his email:

When I saw this question posed in an article about you, I hesitated to send this email because I assumed that my reply was the commonly accepted and well-known explanation.
The explanation I was told is that nodding the head is simply a vestige of bowing down (i.e., agreeing or acquiescing to the statement expressed).
Shaking one's head would therefore simply be an opposite movement to that signifying agreement.
Of course, one clue to whether this is a valid theory would be the answer to the question: "Is nodding/shaking one's head to signify yes/no common to all cultures? Or is it more prevalent in cultures where bowing down is or was part of the culture?"

Bowing as a signal of subservience is culturally bound, but wouldn't a baby's breastfeeding behavior be instinctual? And even if it were, would this translate to a nod meaning yes in every culture?

We don't have to worry about that possibility. Clearly, the nod isn't a universal "yes," even in Western cultures. More than any other country, we heard from Bulgarians, and folks who have traveled to Bulgaria. In Bulgaria, a nod means "no" and a shake means "yes."

Homer Mershon, who speaks Bulgarian, learned that when he was speaking to a native Bulgarian,

I had to learn to pose questions in a way that avoided yes/no answers, since I've always had reciprocal problems and the reverse head movements ended up being totally confusing.

Mershon also indicated that he thinks the gesture "switch" was true of countries neighboring Bulgaria. If my correspondence is correct, Mershon is right. We heard from several folks who claimed that at least in parts of Greece and Turkey, the nod/shake follow Bulgarian rather than American custom.